In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4200 votes. Find the total number of votes casted.
A. 30000
B. 43750
C. 45000
D. 42000
Answer: Option B
Solution(By Examveda Team)
Winner gets 55% of votes As 4% votes were declared invalid so 96% would be the valid votes So, Winner gets 55% of 96% valid votes Winner gets % valid votes = $$\frac{{55 \times 96}}{{100}}$$ = 52.8% votes Loser gets = 96 - 52.8 = 43.2% votes Difference = 9.6% Now, 9.6% = 4200 So, 1% = $$\frac{{4200}}{{9.66}}$$ Thus, 100% Votes = $$\frac{{4200 \times 100}}{{9.66}}$$ = 43750 Hence, Total Voters = 43,750 Alternatively, Let total number of voters were X. Invalid Votes = 4% Valid Votes = 96% Total Valid Votes = 96% of X = $$\frac{{96{\text{x}}}}{{100}}$$ = 0.96X Winner gets 55% of Valid Votes, = $$\frac{{0.96 \times 55}}{{100}}$$ = 0.528X votes Loser gets = (0.96X - 0.528X) = 0.432X Difference = 0. 528 - 0.432 = 0. 096X 0.096X = 4200 ∴ X = 43750Join The Discussion
Comments ( 3 )
Related Questions on Percentage
A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
Tanvir Nabil logic is correct .
Winner get 55% of the casted voted.. not 55% of the valid votes… so the ans is 30000.
Total vote= 100%
Invalid = 4%
Valide= (100-4) = 96%
Winer= 55%
Louder= 96-55=41%
Mergin=winer=louder 55-41=4200
14%=4200
Total casted vote 100℅=4200/14×100
=30000 ans...
PH..- 8444956592...